an alloy of metals is 20% copper. another alloy is 70% copper.how much of each should be used to make 80 gram of an alloy that is 50% copper?
To find the amounts of the two alloys needed to make an alloy that is 50% copper, we can apply a method called the "mixture equation."
Let's assume that x grams of the 20% copper alloy are used, and (80 - x) grams of the 70% copper alloy are used.
Now let's set up the equation for the amount of copper in the final alloy:
(0.20x) + (0.70(80 - x)) = 0.50(80)
Let's solve the equation step by step:
0.20x + 0.70(80 - x) = 0.50(80)
0.20x + 56 - 0.70x = 40
0.20x - 0.70x = 40 - 56
-0.50x = -16
x = (-16) / (-0.50)
x = 32
So, 32 grams of the 20% copper alloy should be used, and (80 - 32) = 48 grams of the 70% copper alloy should be used to make 80 grams of an alloy that is 50% copper.